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Bootstrapping unit root tests with covariates

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  • Yoosoon Chang
  • Robin C. Sickles
  • Wonho Song

Abstract

We consider the bootstrap method for the covariates augmented Dickey--Fuller (CADF) unit root test suggested in Hansen (1995) which uses related variables to improve the power of univariate unit root tests. It is shown that there are substantial power gains from including correlated covariates. The limit distribution of the CADF test, however, depends on the nuisance parameter that represents the correlation between the equation error and the covariates. Hence, inference based directly on the CADF test is not possible. To provide a valid inferential basis for the CADF test, we propose to use the parametric bootstrap procedure to obtain critical values, and establish the asymptotic validity of the bootstrap CADF test. Simulations show that the bootstrap CADF test significantly improves the asymptotic and the finite sample size performances of the CADF test, especially when the covariates are highly correlated with the error. Indeed, the bootstrap CADF test offers drastic power gains over the conventional unit root tests. Our testing procedures are applied to the extended Nelson and Plosser data set.

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  • Yoosoon Chang & Robin C. Sickles & Wonho Song, 2017. "Bootstrapping unit root tests with covariates," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 136-155, March.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:1-3:p:136-155
    DOI: 10.1080/07474938.2015.1114279
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    3. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    4. Omtzigt Pieter & Fachin Stefano, 2002. "Bootstrapping and Bartlett corrections in the cointegrated VAR model," Economics and Quantitative Methods qf0212, Department of Economics, University of Insubria.
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    7. Jitendra Kumar & Ashok Kumar & Varun Agiwal, 2024. "Bayesian Estimation of Multiple Covariate of Autoregressive (MC-AR) Model," Annals of Data Science, Springer, vol. 11(4), pages 1291-1301, August.
    8. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    9. Anton Skrobotov, 2022. "Testing for explosive bubbles: a review," Papers 2207.08249, arXiv.org.
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    11. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
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    15. Ho, Tsung-wu, 2015. "Income inequality may not converge after all: Testing panel unit roots in the presence of cross-section cointegration," The Quarterly Review of Economics and Finance, Elsevier, vol. 56(C), pages 68-79.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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